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Re: [Phys-L] tricks +- principles



On 05/18/2012 06:13 AM, Robert Cohen wrote:

One solution is to provide the "tricks" but, at the same time, teach
them to understand the basic idea of where the tricks come from and why.

That is part of the solution, but far from sufficient.

I do not think this works for many students, as they will continue to
ignore anything other than the "tricks". A lot of students are really
good at "faking it".

Yes. This is disastrous, but why should we expect anything else?
They've lived on a steady diet of mindless tricks for years. They're
doing what they've been trained to do.

So, I guess I am asking whether a better solution would be to simply
remove the "tricks" from the student's arsenal. Yes, teach them how to
solve problems without the tricks. But don't provide students with
anything that could be potentially used as "tricks."

I don't think that works. I don't think it is necessary ... or
possible ... or even desirable to "remove" tricks. IMHO the
crucial step is getting students to realize that trick-based
approaches aren't sufficient to solve real-world problems. No
matter how many tricks you learn, it isn't enough.

I suggest that rather than removing any particular trick, remove
the temptation for relying on tricks. Specifically, I suggest
choosing sufficiently-complex assignments so that relying on the
principles is obviously easier than memorizing all the special
cases.

Nine years ago, on Thu, 6 Mar 2003 11:09:48 -0500 Joseph Bellina
wrote:

I'm reminded of a tale a friend of mine told me. After graduating from
college and ROTC he chose to go to the Army electronics school. As a
pretest he was asked what are the three most important laws of
electronics. Well he thought about that a while and chose j=sigma* rho,
and Kirchoffs laws. As it happened what they expected was
V=IR, I = V/R and R = V/I

Just the other day, I saw a version of that embodied in a poster
on the wall of the local community college. It was one step
fancier, in that it included the equation for power P = V I, so
that there were 12 possibilities:
http://www.etgiftstore.com/images/OhmsMisc/ac_ohms_law_chart.jpg
Apparently you can even get this in the form of a T-shirt:
http://i1.cpcache.com/product/233828450/ohms_law_tshirt.jpg

scary

Agreed. Scary. Horrifying.

We all know that the Rain Man approach fails because the number
of equations that need to be memorized grows exponentially, and
correspondingly the number of situations goes up exponentially,
making it hard to know which equation goes with which situation.

We just need to get the students to realize this. In the long
run, it is incomparably easier to memorize just one form of
Ohm's law and then use algebraic principles to derive the other
forms if/when needed.

I reckon it is essential to design the assignments to drive home
this point.

This is not hard to do. Just add some additional variables. In
the context of Ohm's law, start by including conductance. The
complexity of the equation-hunting approach grows exponentially,
whereas the complexity of the principled approach grows only
linearly:
Ohm's law: 3 versions
Ohm's law plus power: 12 versions
that plus conductance: 22 versions

If you add several more variables (such as length, area, resistivity,
current density, and electric field) the equation-hunting approach
becomes obviously infeasible. No poster on earth, no T-shirt on earth
is big enough to carry all the possibilities.

From our point of view as teachers, it is easy to come up with
assignments that are complicated enough to defeat the Rain Man
approach; the hard part is keeping the early assignments from
getting /too/ complicated.

The familiar watchword here is "building blocks". The building-block
approach says we should teach a complicated task by first breaking
it down into simpler elements. We teach each element separately ...
and (!) then gradually put the elements together until the student can
handle the complete task.

The second part -- the re-combining part -- is important! Learning the
elementary steps is not sufficient.

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

I hope nobody is going to claim the students "can't" handle this level
of complexity. I just don't buy it. I have here a box containing a
checker-board and checkers. It says right on the box: For ages 5
and up. Five-year-olds can't play checkers very well, but most of
them /can/ play it. The game involves strategy. It involves
sequencing, i.e. combining a series of simple elements to handle
a complex situation, working toward a distant goal. I would hope
that ten years of schooling would make students better at this, not
worse. Otherwise there is something desperately wrong with your
schools.

The same goes for other sports and games, many of which involve
tremendous complexity. The conspicuously deductive game "Clue"
is rated 8 and up ... and there is a "Clue Jr" version for the
5 to 8 year olds. Similarly, ordinary tasks such as driving a
car involve tremendous complexity, with billions of possible
situations.

In contrast, the equation-hunting approach seems to be predicated
on "recognizing the situation" and predicated on the assumption
that if the problem can't be solved in one or two steps it can't
be solved at all. This is crazy.

This is a /fixable/ problem. I reckon the fix revolves around
making the assignments slightly more complicated.

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

Note that sometimes the principled approach is appropriate, and
sometimes not. Here's a favorite example: If a young kid asks
how to turn on the lights in the hallway, the appropriate answer
might be "there's a switch just around the corner in the other
room". A detailed first-principles explanation of how wires work,
how switches work, how light bulbs work, et cetera would not be
appropriate. (If the kid wants more-detailed answers, he can
ask additional questions.)

Rutherford once mentioned "stamp collecting" as an example and/or
metaphor for a situation where principles are of limited value.
Somebody can issue a stamp with an arbitrary design, not related
to any other stamp in any logical way.

Physics involves a certain amount of stamp collecting ... less than
most other fields, but still some. For example, consider the speed
of light as expressed in SI units. This is something you need to
know for many applications, ranging from down-to-earth electrical
engineering to theoretical physics, and lots of stuff in between.
The speed of light is fundamental and universal, but the SI units
themselves are based on historical accidents and arbitrary decisions.
I know some tricks for remembering the speed of light, and I don't
apologize for knowing them.

A certain number of tricks and arbitrary facts are necessary. This
is where the spiral approach comes in. Learning almost always must
start with examples, with few if any principles involved. "There's
a switch just around the corner in the other room." Once we have
a few examples in hand, we can spiral back and use principles to
connect the dots.

In the long run, we remember the principles and not the original
examples, which is just fine ... for everybody except teachers.
We need to keep in mind that even though we are experts, we did
not start out as experts. We should remember that beginners
need a certain amount of stamp collecting, just to prime the
pump. The goal is to learn the principles (and how to use them),
but the process for achieving that goal is somewhat indirect.

Bottom line: I don't think that taking away the students' dirty
tricks is necessary or possible or even desirable. I say memorize
all the tricks you want. Just don't expect them to be anywhere
near sufficient for handling the assignments you will see in this
course ... or in the real world.

Building-block approach.
Spiral approach.
Connections.
Real-world applications.