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



On 7/8/2012 1:38 PM, John Denker wrote:
On 07/08/2012 06:06 AM, Jeff Bigler wrote:
Perhaps my engineering bias is showing, but why not explicitly teach
students about making assumptions:

2. What assumptions are usually good in the "real-life" situations most
of us encounter on a day-to-day basis?

3. Which additional assumptions are we making in order to simplify the
problem, even if they make the problem no longer representative of what
happens in most "real-life" situations?

from the student point of view, the situation is not nearly
so cut-and-dried. It's necessary but not sufficient for students to
hear what needs to be done. The hard part is learning /how/ to do it.

There is a problem with item (2) in the list above. The problem is
that there are infinitely many assumptions that we make on a day-to-day
basis. It takes experience and judgment to determine which assumptions
are worth questioning, or even worth mentioning.

I emphasize that many of these assumptions are utterly nontrivial.

This is related to one of the fundamental rules for how to make decisions (in
science, in business, et cetera). The rule is to consider all the /plausible/
hypotheses. You cannot possibly consider all hypotheses without restriction.
Alas it takes judgment, intuition, and common sense to decide what's plausible
and what's not.

It's necessary but not sufficient to tell students this needs to be done.
The hard part is teaching them /how/ to do it.

Completely agreed. The "what assumptions are usually good" and "which
additional assumptions are we making" need to include the idea that
we're only looking at plausible hypotheses and assumptions that are
plausibly likely to be able to affect the outcome in a measurable way.

In a high school course, we need to start with assumptions that the
students can understand, which depends on their awareness of the
components of the situation, their knowledge of what can affect those
components and the situation as a whole, their understanding of what's
measurable/significant and what's not, and their ability to understand
the connections in a quantitative or qualitative manner, as appropriate.
Given the poor number sense that many of today's high school students
have, this is much more difficult for them than it was for high school
students of a generation ago.

Also, the assumptions a high schooler might be able to recognize and
describe in September are, I hope, different from the ones he could
recognize and describe in April, and are different still from the ones
he could recognize and describe after taking a college-level physics
course. I wouldn't at any point expect my students to be able to come
up with as detailed a list as someone with a higher-level understanding
of physics could, but even coming up with a few will expand their
understanding of a concept beyond the confines of the neat little box
that we've stuffed it into.

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.

--
Jeff Bigler
Lynn English HS; Lynn, MA, USA
"Magic" is what we call Science before we understand it.