Re: [Phys-L] playing for keeps

[John Denker <jsd@av8n.com>]

On 06/29/2013 06:34 AM, Dan Crowe wrote:

> V = IR, I = V/R, and R = V/I is not a set of three equations: it is a
> set of three representations of one equation.

++ You see it that way.
++ I see it that way.
-- Other people do not necessary see it that way!


On 06/29/2013 06:34 AM, Dan Crowe wrote:

> found a lengthy explanation to help learn "the three equations" of Ohm's Law.

That's what I was alluding to.  But wait, there's more.  If you are
interested in power dissipation (as well as voltage, current, and 
resistance) then there are 24 equations to memorize (not just three).

For only $24.95, you can get a poster to hang in your classroom, to
help people learn all 24 equations by rote.
  http://www.etgiftstore.com/24-classroom-charts-your-choice-of-ohms-law-charts-ac-or-dc-ohms006-detail.htm

There was a time in my life when I could not have imagined any such
poster could exist.  But it does exist.  I regularly attend seminars 
in a community college classroom where such a poster hangs on the
wall.  It's for the "avionics technician" training program.  This is 
a /postsecondary/ training program.  You might think that high-school
algebra would be a prerequisite, but it is not.

You can understand the situation as follows:  Some of these students 
don't understand algebra, and this program is not going to teach 
them algebra.  It teaches them how to plug numbers into a formula, 
not how to perform abstract manipulations on algebraic symbols.

I reckon at least 90% of the students in this program could learn
algebra, and would be better off learning algebra.  However, the
college doesn't want to spend the time and money it would take to
teach them algebra ... and it doesn't want to wash out the 10% or
so who have some disability or phobia that would interfere with
learning algebra.

I know people who are never going to learn algebra.  They are never 
going to be physicists, but they are perfectly nice reasonable
people who hold high-paying professional jobs.  Note that according
to BLS statistics, on average, an avionics technician gets paid
slightly more than a school teacher.

Bottom line:  There are two sides to the argument:
 *) I am glad there is a career path for people who are never
  going to learn algebra.

 *) On the other hand, algebra is a prerequisite for HS and college
  physics.  These students will be better off if we insist on the
  algebraic approach to Ohm's law and everything else, rather than
  the rote equation-hunting approach.

  The rote approach to Ohm's law is a crutch.  People with a
  disability may need a crutch, and I'm OK with that ... but
  everybody else is better off not using crutches.

  This is only the tip of a super-important iceberg, namely the
  idea of teaching them to learn, to remember, and to think.  And
  as explained previously, by "remember" I mean a deep, powerful,
  intellectual, richly-connected memory, the kind of memory that
  is good for figuring things out (not a rote memory).

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

Speaking of figuring things out:

 1a) Can you tell me the mass of the proton, right now, without
  looking it up, accurate to better than 1%?

 1b) If not, can you tell me how much a mole of protons weighs?


 2) What's the square root of 50, accurate to better than 1%?

  I can think of two ways of figuring this out in my head,
  either one of which is faster than using a computer or
  hand calculator.


 3) Given an ellipse with semi-major axis "b" and semi-minor
  axis "a", what's the formula for the area of the ellipse?
  I don't remember this formula, but I can figure it out in
  less time than it takes to ask the question.


 4) How much water flows down the Mississippi in a year?  Pick
  a spot such as New Orleans and tell me how much river water
  flows past that spot.  Figure it out, without looking anything
  up.


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

Sometimes there are techniques that help with this
 -- expanding stuff to lowest order
 -- scaling laws in general;  
    dimensional analysis as a weaker corollary
 -- symmetries and conservation laws
 -- et cetera.

... and sometimes the only thing that matters is the /habit/
of figuring stuff out.  If you do it a lot, you get better
at it.  Education should be about forming good /habits/ ...
habits that remain for the long term.  This is what I mean
by playing for keeps.  If at some point you decide that you 
would rather figure stuff out than look it up, the habit 
reinforces itself.

On 06/28/2013 07:29 PM, Bruce Sherwood wrote:
> Apparently it is well established by experiment that in general forgetting
> follows a fairly universal power law.

Habits are exempt from this law.


On 06/29/2013 09:32 AM, rjensen@ualberta.ca wrote:

> You look up data! (And numerical data changes over time.) 
> I don't ask my students to memorize physical constants, I teach
> students where to find the data and how to assess the quality of the
> data. 

Sometimes you look up data ... but sometimes it's quicker and better 
to figure it out.  Figuring stuff out is a good habit, because it 
allows you to see the relationships between things.

At the 1% level of accuracy, the mass of the proton does not change
over time.

Some people say that principles should be learned, and details can be 
looked up whenever necessary ... but the concept of /figuring stuff out/
blurs the distinction between principles and details.
 -- The mass of the proton is a detail.  It could be googled.
 -- The definition of dalton is worth remembering.  There's a concept
  involved, something to do with connecting mass to baryon number in
  atoms.  The mass of the proton is not exactly 1 u, but it's within 
  1%.  Actually it's off by about 0.7%, which is interesting unto itself, 
  because it tells you something about the order of magnitude of nuclear
  binding energies.

It is good to cultivate the /habit/ of figuring stuff out.  If you are
stuck waiting somewhere, practice figuring stuff out.  
 -- How many ways can you think of for figuring out the square root of 50?  
 -- How many ways can you think of for proving the Pythagorean theorem?  
  Hint: I've seen about 100 different proofs.
 -- What's the density of air?  What's the mean free path?  How is 
  the speed of sound related to the speed of smell (i.e. the rate of
  diffusion)?
 -- Why are meteor showers typically best seen in the wee hours of the
  morning?