Re: [Phys-L] routine assumptions and plausible hypotheses ... or not

[Hugh Haskell <haskellh@verizon.net>]

At 3:22 PM -0400 7/8/12, Jeff Bigler wrote:
> In fact, I think most of the value is in the exercise of *thinking*
> about assumptions, and about some of the limits on what students can
> calculate in homework problems, on tests, etc.  Then, when they're
> taking one of those telepathy exams, they have some of the tools they
> need to respond when they overthink the question.  (By "overthink", I
> mean something to the effect of "consider the problem in a broader sense
> than the questioner intended".)  If a student can say, "Assuming we can
> neglect the mass of the spring and the coefficient of friction of the
> ice, the mass of the puck does not matter," then he can be confident of
> his answer.  If the student correctly guessed the questioner's
> assumptions, he got the correct answer.  However, if the questioner was
> looking for a problem that considered either the mass or the friction,
> he has shown that he has at least some understanding of how the
> quantities would be applied to the problem.  This is the thinking that
> goes on in the minds of many of the students who overthink
> problems--"what if ________ matters, even though my gut instinct is to
> assume that it doesn't?"  Of course, this presupposes that the student
> can, in fact, tack an open-ended response onto a multiple-choice
> question--that's a rant for another time.
Combining the thoughts of both JD and JB, I would suggest that a 
reasonable way to approach this problem would be to a) specify early 
in the course the assumptions (at lest the ones the student should be 
realistically expected to know of), and emphasize them often and 
repeatedly; and b) then on tests ask the students to qualitatively 
estimate the effect on the answer of dropping one or more of the 
assumptions. Which ones to query them about should, of course, be 
only those that the student, at that point in their study, should be 
expected to understand the effects of (eg. don't ask how including 
the effects of a rotating earth on a trajectory will affect their 
answer to the problem until after they have studied rotational 
motion). At more advanced levels one could then include the 
cumulative effects of offsetting assumptions, which would require the 
students to understand the relative importance of different 
assumptions.

It could also be worthwhile to bring up some of those situations 
where a normally secondary effect can be more important that the 
obvious primary effect, and thus far more worthy of careful 
calculation than would the primary effect be. For example, and object 
falling from a height will, sooner or later in the course of the fall 
be subject to significant effects of air resistance (assuming that 
the fall is from a great enough height). In the case where the 
falling object is a person, the effects of air resistance obviously 
take on overriding importance, so the effect of increasing the air 
resistance (eg, a parachute) will be an important consideration. 
Students can be reasonably expected to give at least qualitative 
answers to follow-on questions about parachutes and air resistance.

So one starts with lot of assumptions that make the problems readily 
calculable (making clear that these are assumptions, that real 
problems cannot always ignore them, but students need to learn to 
walk before they learn to run; it also helps that this is a time 
honored technique in advanced physics--to learn first how to do a new 
type of problem by extending a simpler but similar one, and then as 
one becomes familiar with the nature of the problem, add the 
complexities needed to solve the real problem one at a time, until we 
get predictions that converge on the experimental or observed results.

I guess it might even be possible to make the follow-on another 
multiple choice, but my preference here would be to make the response 
open-ended, which ought to reveal something of the reasoning that led 
to the student's choice of the MC part.

Hugh

--
Hugh Haskell
mailto:hugh@ieer.org
mailto:haskellh@verizon.net

I have been wondering for a long time why some of our own defense 
officials do not
put more emphasis on finding a good substitute for oil and worry less 
about where
more oil is to come from.  Our people are ingenious. New discoveries 
are all around
us, and when we have to make them, we nearly always do.

						Eleanor Roosevelt
						February 13, 1948