[Phys-L] concept mapping; was: wondering about stuff

[John Denker <jsd@av8n.com>]

The overarching theme here concerns the two-step process of
 a) putting ideas and facts into the brain, and
 b) getting them out again.

This are of course closely related, but they are not the same 
thing.  It seems to me that students are trained to place too
much emphasis on part (b).  They think that getting a good grade
on the test depends primarily on working hard during the test
... whereas in reality it depends to a much greater degree on 
doing wise things in the months and years leading up to the
test.

The games described below are not usually very useful for 
solving any /particular/ short-term problem ... but instead 
they are useful as a way of laying down a broad and deep 
foundation that helps with lots of problems over the long term.

Specifically:  After the test has started, it's waaay too late
to start drawing concept maps and wondering about them.  

The direct approach to problem solving, i.e. endless drill 
and practice, is not sufficient.  A certain amount of /indirect/
activity is also needed.  Loosely speaking this indirect activity
is sometimes called "playing around", but that does not mean it
is in the same category as playing chess or checkers.  With a 
board game, even if you win, it's still just a game, and most 
of the game skills have only limited value in the real world.
In contrast, playing around with the kinematics concept map or 
the wave mechanics concept map is by no means an idle or trivial 
pursuit.

Young children start out with enormous curiosity and wonder.
Perhaps they naturally lose that over time ... or perhaps the
education system squeezes it out of them.  In any case, we
should do more to encourage curiosity, to encourage wondering
about things.  Here is a specific, constructive suggestion.

On 05/22/2013 05:20 PM, I wrote:
> One suggestion is to 
> have the students play a game of Six Degrees of Kelvin Baryon ... 
> i.e. to start with two random physics and find some chain of
> connected ideas that lead from one to the other.

Let's expand on that idea a little bit.  We can visualize 
the structure of the game by using a concept map.

The hyperphysics site is a source of examples:  There is
a lot of interesting stuff on this site, including numerous 
concept maps.  If you look at the maps in any detail, they
are hard to take seriously ... but even so, they are better
than nothing.

Here's a specific example:
Starting from the root
  http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
we quickly arrive at the electromagnetism map:
  http://hyperphysics.phy-astr.gsu.edu/hbase/emcon.html

Note the contrast:
 1) There is a vast literature on concept maps in general,
  as a pedagogical tool and otherwise.

 2a) I have a hard time taking the maps seriously.  Drawing
  a 2D map implies that you think the data exhibits some
  relatively simple topology.  There are conventional ways
  of approximately projecting 3D data onto a 2D map, and 
  there are ways of approximately projecting a tree onto
  a 2D map ... but the general case is a mess.

 2b) Also note that there are so many concepts that you
  need to apply arbitrary filters to keep the map from
  exploding.  Without such a filter, electric charge would 
  be connected to conservation of charge, which would be 
  connected to conservation in general, which would be 
  connected to lepton number, energy,  momentum, angular
  momentum, maybe parity, and maybe entropy ... and within 
  another one or two steps, it's connected to all of physics.

  Also, even with the filter in place, the map shows a very
  incomplete subset of the relationships between the concepts.

Still, it is more useful to think about what value we can 
extract from such a diagram, rather than fixating on what's 
wrong with it.  As the basis for an /informal/ exercise in 
wondering about things, we can ignore the alleged connections 
on the existing diagram.  Instead, we treat it as just a 
grab-bag of concepts, and start drawing our own connections.

A) Specifically:  On the map, pick a concept at random.  Call 
on a student to explain how it is connected to other things.

 -- Electric power is shown connected only to DC circuits
  ... but in reality it is strongly connected to AC circuits, 
  since almost every power plant in the world uses dynamos 
  to generate AC power.  (Fuel cells exist, but they're rare.)
 -- Measurement is shown connected only to voltage and
  current ... but in reality it is connected to EM waves,
  since we can measure the frequency and wavelength.
 -- Electric current should be connected to magnetism.
 -- Charge should be more directly connected to current,
  because in spacetime they cannot be separated.  Not
  coincidentally, this is related to conservation of charge.
 -- The concept of resistor should be connected to Ohm's law.
 -- The concept of "Maxwell's equations" should be connected
  to basically everything else on the page.
 -- For example,the Maxwell equations (on the far right side 
  of the diagram) should be directly connected to Kirchhoff's 
  voltage law (on the far left side of the diagram) ... since
  the latter is a restricted corollary of the former, valid 
  in the DC limit.

Note that as part of the game, one should say /in what way/
things are connected (rather than merely asserting that they
are somehow connected).  Sometimes there is an obvious connection, 
but even then there is value in looking for additional, less-obvious 
connections.

======

B) One can also play a different game by choosing an item from
the list and thinking of something that it connects to that
is /not/ on the map.  For example,
 -- Coulomb's law of electrostatics is isomorphic to Newton's
  law of universal gravitation.
 -- EM waves are connected to radio communication.
 -- EM waves are connected to vision.
 -- EM waves are connected to waves in general, including
  sound, also including quantum mechanics.
 -- Charge and current are related to conservation, which
  connects to all of the other conserved quantities we know.
 -- The equations of electrostatics and/or magnetostatics
  are isomorphic to the equations for the flow of dry water.
 -- Magnetic flux should be added to the map, and connected 
  to magnetic field.
 -- Flux should also be connected to charge, since they are
  dynamically conjugate, in the same way that position is
  conjugate to momentum.
 -- Resistance is related to the fluctuation/dissipation theorem.
 -- et cetera.

When playing such games, one need not start with the electro-
magnetism map;  there are lots of other maps that work just
as well.
  Mechanics map:  http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html#mechcon
  Index to other maps:  http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html
  And lots more on other sites.

==========

Note that both of these games are open-ended.  That is, they 
are not even remotely like multiple-guess quiz questions.
In game A, there is a finite (albeit large) number of pairs 
to check, so that part of the game is not open-ended;  the 
openness comes from the fact that there is essentially an
unlimited number of /ways/ in which the pairs could be related.

Game B is even more obviously open-ended.

In the real world, there are a few genuinely multiple-choice
situations, but there are also plenty of open-ended situations.

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

When playing such games, you can use an overhead projector with
/layers/.  That is, put a blank foil on top of the map, and draw
on the top layer.  Then discard that foil and replace it with
another blank, and so on.  Otherwise you wind up with so many
connections that nobody can see anything.

The same technique works with computer drawing programs.  Learn
how to use the /layers/ feature of your drawing program.  Lock
the layer that contains the main concept map, and scribble on
a higher layer.