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Topic: Difficult stat concepts
Replies: 1   Last Post: Nov 1, 1996 11:14 AM

 Joe H Ward Posts: 743 Registered: 12/6/04
Re: Difficult stat concepts
Posted: Nov 1, 1996 11:14 AM

On Fri, 1 Nov 1996, Laura Thompson wrote:

> Date: Fri, 1 Nov 1996 05:28:35 -0500
> From: Laura Thompson <lthompso@s.psych.uiuc.edu>
> To: Multiple recipients of list <edstat-l@jse.stat.ncsu.edu>
> Subject: Re: Difficult stat concepts
>
> I think one of the reasons why basic probability (problems) are so hard for
> students to grasp is because they don't get enough practice. Why should
> probability be a concept that comes naturally to them? especially
> detailed "objective" problems.
> But how many intro courses can spend a lot of time on it?
>
>

Laura --

I don't have any strong feelings about AMOUNT OF TIME ON PROBABILITY.
However, I do feel that the sequence of dealing with UNCERTAINTY
(PROBABILITY INCLUDED) IS IMPORTANT. The important thing is to convince
students, BEFORE THEY ARE "TURNED-OFF", THAT "THEY CAN DO IMPORTANT STUFF
AFTER THE COURSE THAT THEY COULD NOT DO BEFORE".

We work from, what are call THE BIG-FOUR CONCEPTS :

Prediction, Uncertainty, Modeling, Optimization (PUMO for short).
(The ORDER of listing is only because, to most students, PUMO sounds better
than POMU!)

I have found that it is most logical for first-course students (including
high-school students) to discuss the ideas in the POMU order--eventually
bouncing around the four ideas as appropriate.

PREDICTION is fundamental to what everyone has to do all the time.

OPTIMIZATION involves CHOOSING from among Predicted Outcomes those that
are "best" (MAXIMIZE or MINIMIZE objective functions).

MODELING is useful for discussing the ways that are used to bring the
"relevant properties of reality" into the PREDICTION PROCESS.

UNCERTAINTY involves the many things that influence the accuracy of the
PREDICTION processes. This includes PROBABILITY.

Notice that UNCERTAINTY seems, in my observations from working with
first-course students, to be the last discussion item.

Of course, once these ideas are "on the table", the action jumps around
among all four.

-- Joe

P.S. - These ideas may be of little concern for STATISTICS education.
Perhaps the approach is more appropriate for those interested in
OPERATIONS RESEARCH/MANAGEMENT SCIENCE!

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