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On 08/13/2012 12:20 PM, Turner, Jacob wrote:
I've been banging my head on how to design a lab which will impart a
sense of using inference. I intend this for our lower level
(non-calculus) freshman labs, so should be fitting for AP High School
physics range as well I imagine.
1) I would hope that *all* labs and indeed *all* activities of
every kind would involve lots of inference. This is not something
we do once a year on National Inference Day ... it is something we
do all day every day.
2) As usual, I am not interested in fussing with the terminology ...
except insofar as it affects the understanding.
In this case, it seems that most people who answered this question
took it to be a question about /induction/ ... i.e. learning a rule
If that was the intended meaning, we can continue down that road,
if we want, but we should call it /induction/.
On the other hand, perhaps the question might have been -- or should
have been -- about inference in general, about reasoning in general.
Inference aka reasoning covers a lot of ground, including:
-- deductive inference (aka deduction) (including formal syllogisms),
as well as
-- inductive inference (aka induction) (including learning from
For a long discussion of how to teach (and learn) reasoning skills
in general, see
It is worth noting that /under favorable conditions/ learning from
examples can be every bit as rigorous and reliable as classical
syllogistic deduction. There is a vast "overlap" region where it
is pointless and/or impossible to distinguish the two.
When learning from examples, much depends on the size (S) of the
hypothesis-space that must be considered. If S is finite, the
correct rule can be learned using a correspondingly finite number
of examples. If S is infinite, learning-from-examples is guaranteed
to fail. There are theorems about this.
An example of a clearly finite problem is the "Twelve Coins" puzzle.
An example that is less obviously finite, but still definitely finite
if you look at it the right way, is the "Twenty Questions" parlor
The Eleusis game does not have any obvious upper bound on S. It
depends on how diabolically devious you think the "dealer" is.
Ditto for the "black box" circuit puzzle ... unless you announce
in advance some restrictions on the complexity of what's in the
Keep in mind that curve fitting (which the students "should" have
seen in high-school chemistry) is a form of inductive inference.
I like Bongard problems. They do not require any "domain knowledge"
beyond grade-school notions of geometry, which makes them usable
on the first day of class. There are enough of them that you can
do a few in class and still have plenty to assign as homework.
This runs the risk of failing to
think of some easy approaches,
Indeed! One of the cardinal rules of critical thinking is to
consider *all* of the plausible hypotheses. There exist huge
collections of puzzles and riddles that require out-of-the-box
thinking. You could start with the eponymous nine-dots puzzle
and maybe the fox-duck-grain puzzle. Again, see
and references therein.
The primary obstacle is that this is intended for the first week in a
first physics course for students who likely have many unfamiliar with
any form of scientific thought.
Yeah, that's a huge problem. The even bigger problem is diversity:
*some* of the class will know how to attack reasoning-intensive
puzzles and some of them won't.
The wily teacher has ways of dealing with this, but there's nothing
easy about it.
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