Re: [Phys-l] thoughts for future physics regents.

[John Denker <jsd@av8n.com>]

On 06/21/2011 04:15 PM, Michael Barr wrote:
> thanks for the advice.

:-)

Interesting topic!

> my main problem thought is that some of the weakest kids can do the algebra
> and get it pretty well however when confronted with doing algebra with
> letters (aka units) its like reading Greek.        [a]

> Sadly, not all of my students
> would know for sure that an energy question is going to have a Joule unit.
>  Most do, but they are not the ones losing points left and right.    [b]

OK!  Those are two important observations.  They point to problems
that are relatively benign and fixable.

a) I don't want to make a big deal about terminology, but in my book
 algebra "with letters" is called simply algebra.  Algebra minus the
 letters is just arithmetic, n'est-ce-pas?

 I mention this because in an algebra-based physics course, ability
 in algebra is "supposed" to be a prerequisite.  More importantly,
 even if the students can't handle algebra at the start of the course,
 the really ought to be able to handle it at the end.  It's a course
 completion requirement (even if it isn't an enforceable enrollment
 requirement).  It's one of the reasons college admissions committees
 want to see "physics" on the transcript.

 This is relevant because the Regents *ought* to be testing for this.
 It's sorta the point of the test.  If the students can't do algebra 
 competently, IMHO they *should* be losing points left and right.

 One could argue that it's not fair to expect the physics teacher to
 teach algebra *and* physics, but as the saying goes, life isn't fair.

 If life were even halfway fair there would be a placement test just
 before the start of classes, and students who didn't have the required
 background would be enrolled in remedial math, not physics.

 At the other extreme one could argue that an integrated approach to
 algebra and physics makes more sense than doing either one separately.
 The physics motivates the math, and the math provides the skeleton
 and the sinew that holds the physics together.  Bear in mind that a 
 good bit of what we consider mathematics was invented by physicists.

 There are lots of algebra-based physics texts.  In jest I suggest
 somebody should write a physics-based algebra text :-) 

 By way of context I note that at the upper-division undergraduate
 level, there are courses (and books) on "Mathematical Methods of
 Physics".  In all seriousness:  At the HS level I would like to 
 see an /integrated/ algebra+physics book (or pair of books).

b) This is an even more interesting observation.

 As I have mentioned before, units and dimensions are part of a
 larger topic, namely scaling.  (Every dimensional argument is
 also a scaling argument, but not vice versa: there is such a
 thing as non-dimensional scaling, but we don't need to get into
 that just now.)

 Scaling laws have been part of physics since Day One of modern
 science (1638) ... and are still important:
    http://www.google.com/search?q=scaling+site%3Anobelprize.org

 Scaling is not mentioned on the typical syllabus, but IMHO it
 should be taught anyway.  It is *easier* than most of the stuff
 that is on the syllabus, and more age-appropriate ... and it is
 treeemendously powerful.

 For example:  Remind the kids that if you start with a square 
 and make every edge 5 times longer, the area goes up by a factor 
 of 25, i.e. 5 squared. Then ask them what happens if we take a 
 /triangle/ and make every edge 5 times longer.

 It's amazing how many kids -- and how many adults -- get this
 wrong.  This stuff is easy to learn, and very very useful.

 Not coincidentally I ask:  What is the sum of the first five
 odd numbers? 

 Galileo knew this stuff.  High-school physics students should
 know this cold.  Call on some random student and ask, What is 
 the sum of the first ten odd numbers?  How do you know?  Can
 you draw the picture?  Ask again, day after day, until they 
 all know it cold, and know how it is related to geometry and
 physics.

   My answer:  For any arithmetic series, the sum is
      (first term + last term) * (number of terms) / 2

   It's the area of a triangle.
    http://www.av8n.com/physics/img48/arithmetic-series.png

   It's related to scaling, because as the number of terms
   in the series increases, the diagram gets wider /and/ 
   taller.

   (Other equally-good answers abound.)

 This stuff can be learned and can be taught.  You can
 easily test for it

 As a more physics-related example:  The field of a point
 charge falls off like 1/r^2.  This can be understood (and 
 visualized!) in terms of the continuity of field lines,
 plus a basic scaling argument (area of Gaussian pillbox
 scales like r^2).

 Dozens of additional examples can be found at
  http://www.av8n.com/physics/scaling.htm#sec-misc

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

To recapitulate my previous note:  When a kid gets a question
wrong on the Regents, that is a symptom.  All-too-often, the
symptom is only a distant reflection of the underlying fundamental
issue.  It takes a lot of artistry to figure out what the real
issue is.  Sometimes a symptom means almost nothing, for instance
on a multiple-guess test where there is no penalty for random
guessing.  Sometimes I need to see five or ten symptoms before
it dawns on me what the real issue is.  In general, my advice 
is to not worry too much about any particular "symptom du jour" 
but rather to stick to the fundamentals.

A short list of fundamental learning and problem-solving skills
can be found at
 http://www.av8n.com/physics/thinking.htm#sec-basic

There's probably quite a lot that I have inadvertently left off
that list;  suggestions would be welcome.

Some useful hints for gaming the test can be found at
  http://www.av8n.com/physics/thinking.htm#sec-gaming