Re: [Phys-L] widget rate puzzle ... reasoning, scaling, et cetera

[John Denker <jsd@av8n.com>]

On 01/02/2015 07:22 AM, Philip Keller wrote:
> If you present these variations to these students, you run the risk
> of them throwing up their hands in surrender. They are already
> functioning at the edge, not completely convinced that thinking is a
> way to find things out.

OK, thanks, that calls attention to another two or three 
parts of the elephant.  Here's how I about these parts:
  https://www.av8n.com/physics/img48/hard-or-not.png

 -- The original widget problem is in the upper-leftish
  orange region.  The student thinks the problem is easier
  than it really is, and is tempted to be overconfident.

 -- The "surrender" situation is the lower-rightish red
  region.  The student thinks the problem is harder than
  it really is, and is tempted to panic.

Starting with the widget puzzle, we want the student to 
learn to be careful even when the problem looks simple,
even when it is simple.  One way of doing this is to 
expand the "methodical" region downward and leftward,
so that methodical approaches apply even to seemingly
simple problems.  

The other way is to move horizontally in the diagram,
i.e. to make the problem seem harder, i.e. make it
look as hard as it really is.

However, if we make the problem look too hard, we get 
the opposite kind of trouble, namely panic.  That's not
good;  it just substitutes one misconception for another. 
We want the student to learn to use proper problem-solving
skills always, no matter whether the problem seems hard
or easy or somewhere in between.

Note that as we move along a line from overconfidence 
to success and then to panic, the effect is non-linear, 
indeed non-monotonic.  It is not good to overestimate 
/or/ underestimate the difficulty of the problem.

There is a proverb that says:
  Education is the process of cultivating your intuition.
In the diagram, education causes the "good intuition"
region to grow and extend farther toward the upper-right
corner.

If the student has a weak background, the good region in 
the diagram might be thin or nonexistent;  in that case
the student could lurch from overconfidence to panic.  The
obvious remedy is to learn more problem-solving skills, 
so that "trivial" and "impossible" are not the only two 
possibilities.

The stuff that is already intuitive is the stuff that you 
don't need to teach, so there is a partially-reasonable 
tendency for teachers to focus on the counterintuitive 
stuff.  HOWEVER the fact remains that the vast majority
of intuition is good.  I mention this because in some of
the PER literature "intuition" is used as a synonym for
"misconception", which makes me want to tear my hair out.
If students have a weak background, they need more and
better intuition, not less intuition.

Selecting the examples to be always counterintuitive 
creates a ghastly distortion of the topic.  One should
always start with some nice intuitive examples.
 -- Learning proceeds from the known to the unknown.
 -- Education is the process of cultivating your intuition.

===========

Meanwhile, we should keep in mind that hard-versus-easy 
is not the only variable or even the most important
variable.  Students will work a lot harder if they see
the task as worthwhile, amusing, or at least interesting.

There is a huge body of PER literature that looks only
at the hard-versus-easy dimension to the exclusion of
all else, including motivation.  IMHO this seems like
a treeeemendous mistake.

See anecdote below.

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

Returning to this:

> not completely convinced that thinking is a
> way to find things out.

As I have said before:  Keep in mind that by the time
they show up in physics class, the students have been
thoroughly trained not to think.  On the typical high-
stakes multiple-guess test, any question that cannot
be solved immediately should be skipped.  That's the
standard good strategy.  In other words, every item is 
either trivial or impossible.  The students are perfectly
capable of thinking, but that would take time, and they
have been trained not to do it on the test.

  They have also been trained not to think in class or
  on the homework, because that would lead to originality
  and non-conformity, which is not allowed.

If you tell them you are changing the rules, they simply
will not believe you the first eleventeen times you say
it.

This also makes contact with the previous discussion 
of the building-block approach.  An individual physics
concept is not interesting, in the same way that an
individual Lego block is not interesting.  Such things
only become interesting when you combine a bunch of
them to construct something.  All of the thinking, all
of the creativity, and all of the utility depends on 
putting them together in a nice way.

This is why it pains me to see that "conceptual physics"
has become a synonym for "bonehead physics".  There is
too much gawking at individual isolated physics concepts,
and not nearly enough putting them together to construct
useful and interesting stuff.

For end-of-chapter problems, nobody really cares about
the answer, so there is no incentive to be clever, and
students are well aware of this.  There is an obvious
alternative:  As soon as you start doing something real, 
suddenly there is an incentive to be clever about it. 
Mother nature rewards thinking, even if the end-of-chapter
answer key does not.

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

True story:  One day in mid-December many years ago my
mother was driving around on a shopping trip with four
kids in the car.  In the middle of nowhere we got a
flat tire.  Calling a tow truck would have been very 
expensive, and it wasn't even totally obvious how to 
get to a phone.  My mother had a pretty good idea how
to change a tire, but she wasn't going to do it herself,
because she was recovering from a dislocated shoulder.
So it became my job.  The spare tire weighed far more
than I could lift, so it took some fancy leverage to
get it out of the trunk.  The GM OEM lug-wrench was
useless.  However, I noticed that there was a 28" long
breaker bar in the bottom of the spare tire well.
That still didn't solve the problem.  I had always
been big for my age, but the age in question was 6.
I weighed 50 pounds at most.  The lug nuts had been
put on with an air impact wrench, and they had picked
up some rust since then.  My strength was not going
to get the job done.  However, I also noticed that
there was a 30" piece of steel pipe in the spare tire
well.  I wondered what a piece of rusty old pipe was
doing in the car.  It seemed a remarkable coincidence
that it was exactly the right diameter to slip over the 
end of the wrench.  That gave me more than four feet of
lever arm.  I jumped on the end, and !KLUNK! the bolt 
moved a little bit.  And so on.......

That evening it was explained to me that money did
not grow on trees, and not paying for a tow truck
meant that everybody was going to get much nicer
Christmas presents.

  This also tells you something about my father.
  He was big and strong, so he didn't need a snipe,
  but nevertheless he had gone to a lot of trouble 
  to make one and put it in the car.

I was always curious about physics, but it was not
just an idle curiosity.  Real-world utility is the
best motivation, and the best mnemonic.
 -- I suppose you could make a multiple-guess quiz
  question about mechanical advantage, but the actual
  "feel" of jumping on the snipe is something else 
  entirely.
 -- I suppose you could make it part of the course
  "grade" (whatever that means), but having four or 
  five people actually depending on you to get the 
  job done is something else entirely.

Also:  When faced with a problem with multiple steps,
each of which looks like it might be intractable,
don't surrender.  Figure it out.