Re: [Phys-l] ivory windmills

["Robert Cohen" <Robert.Cohen@po-box.esu.edu>]

I don't disagree with the main point but it seems to me that the sig fig examples serve to illustrate the problems with rounding intermediate steps, not the use of sig figs at the end.  Am I mistaken?


Robert A. Cohen, Department of Physics, East Stroudsburg University 
570.422.3428   rcohen@esu.edu    http://www.esu.edu/~bbq 


-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of John Denker
Sent: Wednesday, April 11, 2012 5:20 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] ivory windmills

It has been pointed out, off-list and on, that my previous post was somewhat unbalanced.  Let me try to restore some balance.

IMHO the goal of the educational system as a whole is to prepare students to do well in real life.

So ... suppose at the end of the chapter X there are 40 exercises.  Suppose exercises 1 through 32 are cut-and-dried building blocks that deal with concepts covered in chapter X, one concept at a time ... while exercises 33 through 40 are more open-ended and integrative, including stuff from previous chapters and (!) maybe even stuff from real life.

That's all fine.  Building-blocks are necessary.

However, my point is that the building blocks are not the goal;  they are necessary _but not sufficient_ in order to reach the goal.

Therefore much depends on which exercises the students actually do.  In particular, suppose you assign ten of the exercises, namely 4, 8, 12, 16, 20, 24, 28, 32, 36, and 40 ... and the student actually finishes all but the last two ... IMHO that doesn't count as 80% success but rather as no success at all, because the whole point of the assignment, and the whole point of the educational system as a whole, is for the students to learn to handle real-world problems.

By way of analogy:  Suppose a certain flying student has learned to use the rudder (in isolation), use the ailerons (in isolation), use the throttle (in isolation), et cetera.  Alas, the student cannot integrate those things well enough to land the plane.  You don't really want me to sign that person off as qualified to be a pilot, do you?

Building blocks are fine.  They are necessary.  I spend a *lot* of my time racking my brain trying to find ways to break complex ideas into explainable chunks ... but all that counts for nothing if we just move "towards" 
the goal without actually achieving the goal.

On 04/11/2012 12:12 PM, Aburr@aol.com wrote:
> As one  who has and is writing homework problems, it is hard enough to 
> write correct,  clear, and relevant restricted concept ones.

I agree.  I never said any of this is easy.  Teaching is hard.  Good teaching is really, really hard.

I've spent unreasonable amounts of time (recently and
otherwise) trying to come up with good pedagogical examples that involve numbers that are significant in the Nth digit but uncertain in the first or second digit, e.g.

       ⎛   1.497925297894696 ... ⎞
  X =  ⎜ ± 0.1                   ⎟
       ⎝                         ⎠

The problem is not a lack of real-world examples.  The problem is that most of the real-world examples are so complicated that the roundoff issue gets lost.  There's not much point in talking about "big eigenvalues" and "small eigenvalues" to a high-school student who has never heard of matrices.

I'm reasonably happy with the signal-averaging example,
  http://www.av8n.com/physics/uncertainty.htm#sec-extracting
which is a rather mild example, insofar as only a couple of "extra" digits are needed to solve the problem:

I'm also reasonably happy with the pH example,
  http://www.av8n.com/physics/uncertainty.htm#sec-ph-quadratic
since
 -- It requires lots and lots of "extra" digits,
 -- It is a 100% unadulterated real-world application,
 -- It is IMHO an /interesting/ application.
 -- The term that is in danger of being wiped out by roundoff
  is not some minor correction term;  it is the entire answer.
 -- It requires nothing more than high-school math.
 -- There are multiple ways of getting the answer, each of
  which illustrates a technique that is portable to other
  real-world applications.

I am verrry aware that examples like this are not easy to come up with.  But still, it needs to be done.  Anything less defeats the purpose of the educational system.

> Those types of
> more general  and inclusive problems are more appropriate (indeed 
> necessary) on final exams  and employment interviews.

I 100% agree that comprehensive, real-world problems are appropriate and necessary on final exams and job interviews ... but my point remains:  We want to arrange the training so that everybody knows /in advance/ that the students will do well on the job interview, and (!) on the job thereafter.

That means they need lots of practice with open-ended, integrative exercises all through the year ... indeed all through the years, plural.

Also, a point about metacognition:  The students need to be told what is going on.  They need to be told what the actual goal is, and then told how the various building blocks contribute to that goal.
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