In article <[EMAIL PROTECTED]>,
Bruce Weaver <[EMAIL PROTECTED]> wrote:
>On 20 Sep 2001, Jay Warner wrote:
>> true math phobes may not like the idea of putting the equation details &
>> number crunching up to software. the thinking involved in Dennis' list above
>> is much harder.
Even BC (before computers), it was not that important for
the user of statistics to be able to do the calculations.
However, setting up the problem is what is important.
>> But I'd like to see what happens if a class could let go of the numeracy
>> issues, and look at what is happening - the logic of the questions. Wonder if
>> 'learning theory' can address the possibility of that happening.
I question the use of "logic" here. It is not totally
incorrect, but it does not fit into the framework of any
kind of logic course. What is involved is the ability to
use precise symbolic language, which is sadly lacking,
even in those who have had computational mathematics classes.
The general use of variables belongs with beginning reading;
it is an augmentation of language.
>Jay's last paragraph reminded me of something I question just about every
>time I teach an introductory stats class: Why the heck have we made
>successful completion of a 1st year math course the prerequisite in so
>many cases? Certainly for intro stats classes aimed at non-math majors
>(e.g., psychology & social science students), the level of mathematics
>often does not go much beyond cross-multiplying to solve for an unknown,
>and maybe coming to grips with logarithms.
Why do they have to SOLVE equations? What is needed is the
ability to take a complex problem, and FORMULATE the problem
in symbols. Also, they do not need to know HOW to add or
multiply, but what it means. The same holds for logarithms;
you will find that most students, even with much more than a
year of college mathematics, do not understand logarithms as
exponents, but just as something to manipulate formally, and
to use for calculations.
I think that many of the
>number haters can be helped over those hurdles. I think a greater problem
>for intro stats students is understanding the LOGIC--the logic of
>hypothesis testing, for example. (Some readers of this group might call
>it the illogic of hypothesis testing, of course.) So in my opinion, a
>BETTER prerequisite, if we must have one, would be a course in symbolic
>logic. Just my two cents.
A course in symbolic logic at the sentential calculus level
will not help. At the predicate calculus level it might, but
few have had this, and this is again not what is needed. This
can be taught in elementary school (it has been), but finding
teachers who can learn it might be a problem.
What is needed is first to be able to use variables as the
linguistic entities they are; it has nothing to do with
mathematics. Secondly, they need to understand what the
operations mean, and be able to formulate arbitrarily
complicated problems with no idea of how to solve them;
I would make this the "mathematics" requirement for college
entrance, and at this time, most college graduates cannot
do this. Third, to do anything intelligent with statistics,
they need to understand the probability CONCEPTS, not the
computations or equations. They do not need to know the
formula for a binomial distribution or a hypergeometric
distribution; they need to know when these occur. One of
the problems with students (and even PhD philosophers) is
that they assume equally likely far too often; avoid this.
How many people with statistical problems realize that there
are probability assumptions involved? And if they do, are
they aware of which are the important ones? Transformations
to make things normal are common, but they are likely to
destroy whatever reasonable relations hold, and it is usually
the case that normality is of little importance.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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