Re: [Phys-L] playing for keeps

[Ken Caviness <caviness@southern.edu>]

Question for JSD!  What method do you use to almost immediately figure out the mass of the proton within 1% accuracy, so you haven't had to take the time and trouble to memorize it?  Tantalizing hint (can be done in less time than it takes to ask the question), but I'm drawing a blank -- unless you remember other things more easily, and find m_p from them?  (For example, the m_p/m_e ratio, or the nuclear magneton, or ....)

Good thoughts!

In University Physics, I tell the class about my surprise when I picked up a ham radio test review book and found a lengthy explanation to help learn "the three equations" of Ohm's Law.  They showed a circle, bisected horizontally, with the lower half bisected again, vertically.  The letters V, I and R were placed in the three areas created, V on top, I R below.  Then they said to cover up with your thumb whatever you were trying to solve for.  Covering up the V left I R side-by-side (multiplied), covering up the I left V over R, etc.

Cute, but my point (and yours) is that there is absolutely no need to learn 3 equations in any case.  

KC

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of John Denker
Sent: Saturday, 29 June 2013 1:12 AM
To: Phys-L@Phys-L.org
Subject: [Phys-L] playing for keeps

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.

Only if you let it!

My understanding of this issue has been tremendously improved by the recent discussions.
 -- Until about an hour ago, I would have said something like
  this: There is always a tendency to teach to the test.  That's
  either a good thing or a bad thing, depending on the test.

 -- Until about an hour ago, I would have said that when training
  private pilots, I teach to the test, and am happy to do so,
  because it's a good test.

Now, however, I would like to say something better:  I teach to the /standard/.  I'm playing for keeps.  That is, I want the student to meet the standard on the day of the test, and on the day after, and two years down the road, and twenty years down the road.  This is a much taller order!  Playing for keeps includes teaching to the test, plus a lot more.

I claim I've always played for keeps.  I've always explained this to students.  Recently I've gotten better at explaining it to third parties.

Interestingly enough, the key document is called
  _Private Pilot Practical Test Standards_
  http://www.faa.gov/training_testing/testing/test_standards/media/FAA-S-8081-14B.pdf
so we really do have a standard, not just a test.  The standard controls the test, and not vice versa.  The standard is routinely used for a lot of other things, not just the test.  It's a good standard.

So, how is it possible to evade the allegedly "universal law"
of forgetting?  Well, I confront the thing head-on.  I tell students my job is to put myself out of job.  That is, my job is to get students to the point where they can teach themselves.
I make a very big deal out of this.

Before students can take the practical test, I have to certify that they are ready.  At that time, I tell them that I may not see them again for six months or a year ... but when I do see them, I expect them to fly /better/ than they do now.  I expect them to read, I expect them to practice, and above all I expect them to hold themselves to high standards.  This is not new to them on the day of the sign-off;  we've been talking about it more-or-less every day since the first lesson.

If I thought a guy could meet the standards on the day of the test and not thereafter, I would not sign him off.

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

The same ideas apply to academic subjects such as math and physics, except that people don't take such things nearly as seriously.

All too often, each chapter in the book prepares students to answer the end-of-chapter problems and not much more.  All too often, the course as a whole prepares students to pass the almighty end-of-year test and not much more.

My point is simple:  If you decide that long-term retention is one of the essential goals, then it dramatically changes how you go about teaching.  For starters, you find yourself spending a huge amount of time and effort on mnemonics.  It doesn't matter how true or important or elegant something is, if it will not be remembered.

The textbooks are, by and large, terrible at this.  A good teacher can help a lot, by passing on the mnemonics, the lore, the rules of thumb, et cetera.  However, it doesn't have to be that way.  There's no reason why the textbooks couldn't include a ton of mnemonics.

I insist that things can be learned at more than one level, namely at the rote level and at deeper levels.  If you learn a certain rule by rote, using a five-word mnemonic, it absolutely does not prevent you from learning where the rule came from, including the deep physical principles behind the rule, the provisos, the exceptions, et cetera.
The rote learning and the intellectual learning support each other, if they're done right.

At the end of the year, if you ask the third-grade teacher whether the students learned everything they were supposed to, so that they are fully prepared to go on to fourth grade, the teach invariably says yes, absolutely yes.  Then at the beginning of the next year, if you ask the fourth-grade teacher if the students arrive well-prepared for fourth grade, she says no, absolutely not.

That's /partially/ unfair, because it is partially explained by human nature:  everybody thinks the grass is greener on the other side of the fence, and everybody wishes the other guy would do a bigger share of the work.  However, there is another part that is fair and real.  Imagine how nice it would be if the third-, fourth-, and fifth-grade teachers could all sit down and coordinate with each other:  What can we realistically accomplish?  What do we really need from each other?  More importantly, what do the students really need, long-term?

I say all these teachers should play for keeps.  That means not just teaching the kids stuff in a form that will let them pass the almighty end-of-year test, but rather in a form that will stick with them, a form that will be useful during the next year and forever after.

The same applies to high-school physics and college physics.
We should play for keeps.  If we can't find a way to teach stuff that will actually be remembered, we should give up go home.  We should stop wasting everybody's time.

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

One more thing:  Feynman said that knowledge is like a grand tapestry.  A forgotten fact is like a hole in the tapestry.  You can repair the damage by re-weaving up from the bottom, down from the top, and/or in from the sides.  This is called /figuring stuff out/.

Similarly, William James (1898) emphasized the role of connections as the basis of a good, useful memory.

Physics is so richly connected that it is hard to forget stuff.  It shouldn't stay forgotten for long, because you can figure it out.

As an illustration of what I'm talking about:  If you remember Ohm's law by remembering three different equations
  V = I R
  I = V / R
  R = V / I
then you're doing it wrong.  The smart approach is to learn one of those equations, and then figure out the others as needed, using simple algebra.  Bruce Sherwood makes the same point using a different example:  There is no need to memorize the formula for escape velocity, because you should be able to figure it out in less time than it takes to ask the question.

I have a terrible memory.  I compensate for it by figuring stuff out.  For example, I can never remember the mass of the proton.  I can, however, figure it out, with better than 1% accuracy, in less time than it takes to ask the question.

Bottom line:  There is no point in teaching people physics factoids that won't be remembered.  Instead we need to teach people how to learn, how to remember, and how to think.  If we get students to form the habit of looking for connections and figuring stuff out, we can stop worrying about how to measure memory loss over time.  The students will get smarter over time, on their own.

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