Re: [Phys-L] raising the game

[John Denker <jsd@av8n.com>]

1) Once upon a time, Joe Schmoe bought 10 kilograms of butter.
It was very high-quality, high-purity butter.  For the next 
week, he ate nothing but butter.  He ate butter for breakfast, 
lunch, and dinner.

This illustrates several points:
  a) The buying was /intentional/.  The eating was /intentional/.
    However, that does not make it wise.
  b) There is a question of balance.  Many things that are OK 
    in moderation become quite harmful when taken to extremes.
  c) Sometimes you have to pay attention to what's missing,
    rather than simply checking the quality of what's present.

2) Also:  I'm a big fan of the building-block approach.  That
is, when trying to learn a complex task, you take it apart into
simpler blocks, learn the blocks, and then assemble the blocks
to construct the desired edifice.  A big part of the teacher's
job is figuring out how to take tasks apart and put them back
together again.

The final step -- putting things together -- must not be omitted.
Dealing with the blocks one by one is a fine place to begin, but
it is not an acceptable place to end!

3) The previous two ideas overlap in a way that is relevant to
our recent discussions:  FCI effectively stands for Force Concepts
in Isolation ... and isolation is like butter.  Sometimes butter
makes sense as the first ingredient to go into the pan, but there
are limits.  Dealing with physics concepts in isolation is a fine
place to begin, but must not be the only ingredient in the meal.


On 06/30/2013 08:45 PM, Bruce Sherwood wrote:
>  The intent of
> omitting the algebraic solution was to make [...] stand out in high
> relief. 

I understand that it was intentional.  That does not however guarantee
that it is wise.  See parable #1 above.

For one thing, omitting the step of actually solving the equation
does not make finding the equation harder!  Not in the least.  
These are separate, non-intertwined steps.

Furthermore, solving the equation numerically is less work than 
making excuses for not solving it.  This is 2013, not 1913.  Near 
the end of a year-long course in calculus-based physics, if the 
student cannot use a spreadsheet to solve one algebraic equation 
in one unknown, there is something desperately wrong.

> [...] stand out in high relief

This gets back to the question of balance:  If you pick any 
particular gram of butter, you can argue that that /particular/ 
gram of butter is OK ... and maybe it would be, as part of a 
balanced diet.  However, at some point we need to take a step 
back and look at the overall menu.  I claim it is seriously 
out of whack.

Why does everything students are looking for need to be found
directly underneath the lamp-post, where it stands out in high
relief, brightly lit, in isolation?

Let's be clear:  I'm calling attention to /isolation/, which 
becomes a problem when carried to extremes.  No particular 
homework question or FCI question suffices to illustrate this 
problem;  you need to take a step back and look at the overall
menu.

Also note that the example I picked on was chosen at random.
There is no reason to expect it to be the perfect illustration 
of the point I am trying to make ... except insofar as the 
problem is rather pervasive.  However, while we are looking at 
this example, I must say that isolating the challenging step 
of finding the equation from the trivial step of evaluating 
the equation numerically is conspicuously excessive isolation.

Also:  The cornerstone of critical thinking is "check the work",
and numerical evaluation is a particularly easy way to check
the work.  Human beings can easily overlook a minus sign, but
computers are mercilessly literal-minded about such things.


> It was intended to address
> another important aspect of critical thinking like a physicist, namely that
> starting from a few powerful fundamental principles rather than
> formula-grabbing it is possible to analyze new situations never previously
> encountered, 

I'd be more impressed by that argument if the question did not
provide one of the two key formulas on a silver platter.  The 
only form of thinking lower than equation-hunting is plug-and-
chugging, i.e. lifting an equation from the silver platter and 
turning the crank.

Insofar as the question provides only one of the two key formulas,
finding the answer involves some thinking ... but it has been 
reduced to a one-step thinking process.  Why does every problem 
need to be solvable in one step?  When do students learn how to 
handle multi-step /chains/ of reasoning?

I know the value of the building-block approach, really I do ...
but there are limits.  In the real world, very few of the problems 
that arrive at my desk are solvable in one step.

This is just one of the eleventeen reasons why it would be insane
to use Force Concepts in Isolation as if it were an "indication 
of quality teaching".