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*From*: John Denker <jsd@av8n.com>*Date*: Mon, 13 Aug 2012 19:57:15 -0700

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

from examples.

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

examples).

For a long discussion of how to teach (and learn) reasoning skills

in general, see

http://www.av8n.com/physics/thinking.htm

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

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.

http://www.av8n.com/physics/twelve-coins.htm

An example that is less obviously finite, but still definitely finite

if you look at it the right way, is the "Twenty Questions" parlor

game:

http://www.av8n.com/physics/twenty-questions.htm

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

box.

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

http://www.av8n.com/physics/thinking.htm

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.

**Follow-Ups**:**Re: [Phys-L] Inference Lab Design***From:*"Turner, Jacob" <turner@uidaho.edu>

**Re: [Phys-L] Inference Lab Design***From:*Larry Smith <larry.smith@snow.edu>

**References**:**[Phys-L] Inference Lab Design***From:*"Turner, Jacob" <turner@uidaho.edu>

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