Re: "all accelerations are 9.8m/s^2"

["John M. Clement" <clement@HAL-PC.ORG>]

Teaching logic may not work.  There is evidence that shows that courses in
logic do not actually improve the ability of students to think.  Also
students in grade school are probably not able to comprehend logic, as they
have not yet been able to develop the thinking skills.  Remember that the
transition to formal logic is at age 11+, but few actually make that
transition.  Just because it is included in the curriculum, does not mean
that it is comprehended.  My data shows that math does not seem to raise
student thinking skills much, but physics "can" be effective.

A simple Piagetian test might reveal that your students are actually quite
low.  It is possible to tell them the answers to the test, but a simple
interview reveals that they do not understand the reasoning behind the
answers.  Bringing them up require intensive Socratic dialog, and elicit,
confront, resolve strategies.  See the papers and the book by Shayer and
Adey.  Arnold Arons also mentions this problem in his book.  Significantly
raising average student thinking skills takes about 2 years of work
according to Shayer and Adey, so you have your job cut out for you.  A mini
course is very unlikely to be effective, but a concerted year long effort
may have some benefit.

High Hake gain on the FCI or F&M evaluations may be an indicator of
increased thinking skill as there is a strong correlation between thinking
skill and gain on those tests.


> At 11:36 PM 1/25/01 -0500, Hugh Haskell wrote:
> > every year a certain fraction of my students complete the course thinking
> > that "all accelerations are 9.8 m/s^2! It really makes for some
> > interesting answers to problems.
>
> Innnnnteresting.  That throws quite a dramatic light on the situation.
>
> It seems to me this more to do with basic logic than with gravitation in
> particular, or physics in general.
>
> Specifically, it seems the students in question are missing the crucial
> distinction between
>    a) there exists some acceleration equal to 9.8m/s^2
>    b) each and every acceleration is equal to 9.8m/s^2
>
> Formally this is called First Order Logic.
>    http://www.bestweb.net/~sowa/misc/mathw.htm#Predicate
>
> I would have hoped that all students would have mastered this distinction
> long before starting high-school physics.  Apparently this is true in some
> places, where logic and set theory are introduced in 5th grade
>    http://boston.k12.ma.us/textonly/teach/mathcurric.asp
> but not in other places,
>    http://www.nknox.k12.in.us/nkmath.htm
> where logic and set theory are not mentioned until 11th grade or so.
>
> (This is an example of what I call "same planet, different universe".)
>
> If physics students don't understand this, there's a big problem, and no
> amount of talking about masses or forces or fields or 4*pi*epsilon_0 will
> solve the problem.  The physics teacher will just have to take
> time out and
> conduct a mini-course in elementary logic.  Sigh.